Methods for Constructing Choquet-Capacity Preserving and Ergodic Systems: Examples

Abstract

The Choquet capacity of a random closed set on a metric space is regarded as or related to a non-additive measure, an upper probability, a belief function, and a counterpart of the distribution functions of ordinary random vectors. Unlike the ordinary measures which are additive, Choquet capacities are generally non-additive. The purpose of this paper is to generalize the traditional measure preserving and measure ergodic systems to non-additive settings: Choquet-capacity preserving and Choquet-capacity ergodic systems, by constructing solid and standard capacity systems.